Bearings-only tracking of non-maneuvering target with missing bearings data

In this paper we consider the tracking of a non-maneuvering target using only passively recorded noise corrupted bearings data, in which some of the bearings data may be missing randomly or in continuous intervals over the observation duration. The modified instrumental variable algorithm is used for the estimation of the target trajectory parameters, namely, the course and speed of the target, both of which are assumed to remain constant throughout the observation duration, and the range of the target relative to the observer at the test instant. In case some of the bearings data is missing, the estimation of the target trajectory parameters is carried out with the available bearings only, and no attempt is made to fill in the missing bearings using a pre-processing step. The effect of bearings missing randomly and in continuous intervals is demonstrated in terms of mean square error in estimation of the target trajectory parameters using simulations. It is found that the modified instrumental variable algorithm is able to generate reasonable estimates of the target trajectory parameters without the use of any data pre-processing techniques to account for the missing bearings. Additionally, an algorithm for simultaneous evaluation of error bounds corresponding to the estimated target trajectory parameters is presented using the covariance matrix of the estimator. However, when large number of bearings are missing either randomly or in continuous intervals, the covariance matrix may become non-positive semidefinite. The procedure for estimation of the error bounds for the case of missing bearings is proposed.